The Karlsruhe Dynamo experiment

It has been shown theoretically in the past that homogeneous dynamos may occur in electrically conduct- ing fluids for various vortical velocity fields. Roberts (1972) investigated spatially periodic, infinitely extended fields of vortices which Busse (1978, 1992) confined to a finite cylin- drical domain. Based on Busse's vortex arrangement a con- ceptual design for an experimental homogeneous dynamo has been developed and a test facility was setup at the Forschungszentrum Karlsruhe. The first experiments demon- strated that permanent dynamo action can be generated in a cylindrical container filled with liquid sodium in which by means of guide tubes counterrotating and countercurrent spi- ral vortices are established. The dynamo is self-exciting and the magnetic field saturates at a mean value for fixed super- critical flow rates. The instantaneous magnetic field fluctu- ates around this mean value by an order of about 5%. As predicted by theory the mode of the observed magnetic field is non-axisymmetric. In a series of experiments a phase- and a bifurcation diagram has been derived as a function of the spiral and axial flow rates. netic seed fields to a finite intensity, depending on the con- version rate of mechanical into electrical energy and the dis- sipation rate of the dynamo system. Roberts (1970, 1972) studied analytically dynamo action associated with an in- finitely extended and with regard to two directions spatially periodic velocity field characterized by a velocity scale u and a wavelength 2a. Together with the magnetic diffusiv- ity of the fluid these parameters can be combined in a di- mensionless group, the magnetic Reynolds number Rem = (u · a)/ , to characterize the system. Roberts shows that "almost all spatially periodic velocity distributions in a ho- mogeneous conducting fluid will generate dynamo action for almost all values of the conductivity". Busse (1978, 1992) modified Roberts' dynamo model by introducing a second larger length scale, say the radius r0 (see Fig. 1a). He as- sumes a/r0 1 , and using a scale separation method he derives approximate conditions for the onset of mag- netic self-excitation and the solution for the associated mag- netic field pattern. Introducing magnetic Reynolds numbers for the mean axial and the mean azimuthal velocity com- ponents (uC , uH) in the form RemC = (uC · a)/ and RemH = (uH ·d)/ he finds as a condition for the occurence of an axisymmetric field,